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Polyrhythm: Triplets over duplets in all four beats[1]
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Polyrhythm is the simultaneous sounding of two
or more independent rhythms.
Polyrhythms can be distinguished from irrational
rhythms, which can occur within the context of a single part; polyrhythms
require at least two rhythms to be played concurrently, one of
which is typically an irrational rhythm.

A simple example of a polyrhythm is 3 evenly-spaced notes
against 2, with the 3-beat pattern being faster than the 2-beat
pattern, so that they both take the same amount of time. Other
simple polyrhythms are 5-2, 5-4, etc.

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Another form of polyrhythm would be phrasing to suggest a
different meter than the one being played by the rest of the
ensemble. A common example of this in jazz would be phrasing quarter notes in groupings
of 3 to suggest 3/4 time while the ensemble plays in 4/4. Compare
with hemiola (not a
polyrhythm).

Contents

Usage and
history

Traditional African music, particularly that of West Africa, is known
for its highly complex polyrhythms and, unlike the examples given
below, the downbeats do not usually coincide. Rhythms and counter
rhythms evidence the common African cultural tradition of call and response, with
different drum lines, other musical instruments, bodies and voices
contributing rhythmic elements that complement and communicate with
one another. This element of instrumental, as well as vocalized,
call and response is also evident in the polyrhythmic quality of
jazz, a musical form with its origins in the African
American community.

Nigerian percussion master Babatunde Olatunji arrived on the
American music scene in 1959 with his album Drums of
Passion, which was a collection of traditional Nigerian music
for percussion and chanting. The album stayed on the charts for two
years and had a profound impact on jazz and American popular music.
Trained in the Yoruba sakara style of drumming, Olatunji
would have a major impact on Western popular music. He went on to
teach, collaborate and record with numerous jazz and rock artists,
including Airto
Moreira, Carlos Santana and Mickey Hart of the Grateful Dead.
Olatunji reached his greatest popularity during the height of the
Black
Arts Movement of the 1960s and '70s.

Afro-Cuban music makes extensive use of
polyrhythms. Cuban
Rumba uses 3-based and 2-based rhythms at the same time, for
example, the lead drummer (playing the quinto) might play in 6/8, while the rest of the
ensemble keeps playing 2/2. Afro-Cubanconguero, or conga player, Mongo Santamaria was another percussionist
whose polyrhythmic virtuosity helped transform both jazz and
popular music. Santamaria fused Afro-Latin rhythms with R&B and
jazz as a bandleader in the 1950s, and was featured in the 1994
album Buena Vista Social
Club, which was the inspiration for the like-titled
documentary released five years later.

Among the most sophisticated polyrhythmic music in the world is
south Indian classical Carnatic music. A kind of rhythmic solfege
called konnakol is used as
a tool to construct highly complex polyrhythms and to divide each
beat of a pulse into various subdivisions, with the emphasised beat
shifting from beat cycle to beat cycle.

Common polyrhythms found in jazz are 3:2, which manifests as the
quarter-note triplet; 2:3, usually in the form of dotted-quarter
notes against quarter notes; 4:3, played as dotted-eighth notes
against quarter notes (this one demands some technical proficiency
to perform accurately, and was not at all common in jazz before Tony Williams used
it when playing with Miles Davis); and finally 3/4 time against
4/4, which along with 2:3 was used famously by Elvin Jones and McCoy Tyner playing
with John
Coltrane.

Jimi Hendrix
had the distinct ability to play polyrhythmic melodies on his
guitar during live concerts and jam sessions. This ability was
facilitated by the impressive length and size of his hands, and his
unorthodox fretting method, in which he would maintain rhythm and
lead melodies while using his thumb to fret underlying basslines.
Examples are live concerts from 1968 to 1970, in particular a
performance of "Killing Floor" live at Winterland 1968, an
Improvisation during Woodstock 1969, a solo guitar jam for his song
titled "Valleys of Neptune", among several other recordings.

Nine Inch
Nails front man Trent Reznor uses polyrhythm frequently.
One notable appearance is in the song "La Mer" off of his album
The
Fragile. The piano holds a 3/4 riff while the drums and
bass back it with a standard 4/4 signature. Talking Heads'
Remain in
Light used dense polyrythms throughout the album, most
notably on the song "The Great Curve".

Megadeth frequently
tends to use polyrhythm in its drumming, notably from songs such as
"Sleepwalker" or the ending of "My Last Words", which are both
played in 2:3.

Japanese pop trio Perfume released a single in 2007
entitled "Polyrhythm". The bridge of the song
contains a complex polyrhythm, with vocals in alternating 5:8 and
6:8 against a 4:4 drumbeat, which then changes to 3:2 after a brief
rhythmical hiccup midway through. More confusingly, the low synth
has 14 regular beats over three meausures of 4/4, making for a 7:6
polyrhythm. Perfume's song may well be the most commercially
successful song to contain complex polyrhythms; the single reached
#4 on Oricon's daily singles chart and #7 on the weekly chart,
while the original album "Game" which included "Polyrhythm"
debuted at #1.

Polyrhythm is also called "measure-preserving polymeter",
because there exists more than one meter, but the measure stays
constant. "Tactus preserving polymeter" is used to describe what is
most commonly referred to as polymeter. These terms are found in the
writings of Keith Waters and Steve Larson. Waters' 1996 article
"Blurring the Barline: Metric Displacement in the Piano Solos of
Herbie Hancock" from the Annual Review of Jazz Studies and
Larson's 2006 "Rhythmic Displacement in the Music of Bill Evans"
are two examples.

In Dr. Kagliavanna and the Optical Machine by Cyeniic
Apparatus, the opening/closing sections entail a 4/4 melody in the
bass and piano (Ethan Brauer and Will Bywaters, respectively)
played over a 5/8 hi-hat rhythm (David Belcher).

Examples

The following is an example of a 3 against 2 polyrhythm, given
in time unit box system (TUBS)
notation; each box represents a fixed unit of time; time progresses
from the left of the diagram to the right, although this is
irrelevant since the pattern is symmetric. Beats are indicated with
an X; rests are indicated with a blank.

3 against 2 polyrhythm

3-beat rhythm

X

X

X

X

X

X

X

X

X

X

X

X

2-beat rhythm

X

X

X

X

X

X

X

X

A common memory aid to help with the 3 against 2 polyrhythm is
that it has the same rhythm as the phrase "not difficult"; the
simultaneous beats occur on the word "not"; the second and third of
the triple beat land on "dif" and "cult", respectively. The second
2-beat lands on the "fi" in "difficult." Try saying "not difficult"
over and over in time with the sound file above. This will
emphasize the "3 side" of the 3 against 2 feel. Now try saying the
phrase "not a problem", stressing the syllables "not" and "prob-".
This will emphasize the "2 side" of the 3 against 2 feel. Another
phrase with the same rhythm is "cold cup of tea".

One of the most obvious examples of a 3 against 2 polyrhythm is
the Ukrainian Bell Carol, "Carol of the Bells".

Similar phrases for the 4 against 3 polyrhythm are "pass the
golden butter"[1]
or "pass the goddamn butter"[2] and
"what atrocious weather"; The 4 against 3 polyrhythm is shown
below.

4 against 3 polyrhythm

4-beat rhythm

X

X

X

X

X

X

X

X

3-beat rhythm

X

X

X

X

X

X

As can be seen from above, the counting for polyrhythms is
determined by the lowest common multiple, so if one
wishes to count 2 against 3, one needs to count a total of 6 beats,
as lcm(2,3) = 6
(1234
56 and
123456).
However this is only useful for very simple polyrhythms, or for
getting a feel for more complex ones, as the total number of beats
rises quickly. To count 4 against 5, for example, requires a total
of 20 beats, and counting thus slows the tempo considerably.
However some players, such as classical Indian
musicians, can intuitively play high polyrhythms such as 7
against 8. Polyrhythms are quite common in late Romantic Music and 20th
century classical music. Works for keyboard often set odd
rhythms against one another in separate hands. A good example is in
the soloist's cadenza in Grieg's Concerto in A Minor; the left
hand plays arpeggios of seven notes to a beat; the
right hand plays an ostinato of eight notes per beat while also
playing the melody in octaves, which uses whole notes, dotted
eighth notes, and triplets. Other instances occur often in Rachmaninoff's Piano Concerto No.
2. The piano arpeggios that constitute much of the soloist's
material in the first movement often have anywhere from four to
eleven notes per beat. In the last movement, the piano's opening
run, marked 'quasi glissando', fits 52 notes into the space of
one measure, making
for a glissando-like effect while keeping the mood of the music.
Other instances in this movement include a scale that juxtaposes
ten notes in the right hand against four in the left, and one of
the main themes in the piano, which imposes an eighth-note melody
on a triplet harmony.